I can tell you the what, but not the why! This is how many double daylilies are formed (others have an extra tepal whorl). They are stamens that have what is called "petaloid" tissue on them. Petaloid is an adjective that means something that looks like a petal but isn't. There are pictures of this in the AHS Daylily Dictionary:
Petaloid:
http://www.daylilies.org/ahs_d...
Double daylilies:
http://www.daylilies.org/ahs_d...
They why is some abnormal change in the way a cultivar forms its flowers.